Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667

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1
The greater
city exactly
penſates thegreater
gravity.
SAGR. But do you think that the velocity doth fully make
good the gravity?
that is, that the moment and force of a
able of v. g. four pounds weight, is as great as that of one of an
hundred weight, whenſoever that the firſt hath an hundred degrees
of velocity, and the later but four onely?
SALV. Yes doubtleſs, as I am able by many experiments to
demonſtrate: but for the preſent, let this onely of the ſtiliard
ſuffice: in which you ſee that the light end of the beam is then
able to ſuſtain and equilibrate the great Wool ſack, when its
ſtance from the centre, upon which the ſtiliard reſteth and
eth, ſhall ſo much exceed the leſſer diſtance, by how much the
ſolute gravity of the Wool-ſack exceedeth that of the pendent
weight.
And we ſee nothing that can cauſe this inſufficiencie in
the great ſack of Wool, to raiſe with its weight the pendent
weight ſo much leſs grave, ſave the diſparity of the motions which
the one and the other ſhould make, whilſt that the Wool ſack by
deſcending but one inch onely, will raiſe the pendent weight an
hundred inclies: (ſuppoſing that the ſack did weigh an hundred
times as much, and that the diſtance of the ſmall weight from the
centre of the beam were an hundred times greater, than the
ſtance between the ſaid centre and the point of the ſacks
on.) And again, the pendent weight its moving the ſpace of an
hundred inches, in the time that the ſack moveth but one inch
onely, is the ſame as to ſay, that the velocity of the motion of the
little pendent weight, is an hundred times greater than the
city of the motion of the ſack.
Now fix it in your belief, as a
true and manifeſt axiom, that the reſiſtance which proceedeth from
the velocity of motion, compenſateth that which dependeth on
the gravity of another moveable: So that conſequently, a
able of one pound, that moveth with an hundred degrees of
locity, doth as much reſiſt all obſtruction, as another moveable
of an hundred weight, whoſe velocity is but one degree onely.
And two equal moveables will equally reſiſt their being moved,
if that they ſhall be moved with equal velocity: but if one be
to be moved more ſwiftly than the other, it ſhall make greater
ſiſtance, according to the greater velocity that ſhall be conferred
on it.
Theſe things being premiſed, let us proceed to the
nation of our Problem; and for the better underſtanding of
things, let us make a ſhort Scheme thereof.
Let two unequal
wheels be deſcribed about this centre A, [in Fig. 7.] and let the
circumference of the leſſer be B G, and of the greater C E H, and
let the ſemidiameter A B C, be perpendicular to the Horizon; and
by the points B and C, let us draw the right lined Tangents B F
and C D; and in the arches B G and C E, take two equal parts
B G and C E: and let the two wheels be ſuppoſed to be turn'd

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